Question

find the components of a vector A along two directions making angles alpha and beta with the vector?

Answer 1

The vector OP has initial point at the origin O (0, 0, 0) and terminal point at P (2, 3, 5). We can draw the vector OP as follows:

3D vector

Magnitude of a 3-Dimensional Vector

We saw earlier that the distance between 2 points in 3-dimensional space is

\displaystyle\text{distance}\ {A}{B}=distance AB= \displaystyle\sqrt{{{\left({x}_{{2}}-{x}_{{1}}\right)}^{2}+{\left({y}_{{2}}-{y}_{{1}}\right)}^{2}+{\left({z}_{{2}}-{z}_{{1}}\right)}^{2}}}

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

+(z

2

−z

1

)

2

For the vector OP above, the magnitude of the vector is given by:

\displaystyle{\left|{O}{P}\right|}=\sqrt{{{2}^{2}+{3}^{2}+{5}^{2}}}={6.16}\ \text{units}∣OP∣=

2

2

+3

2

+5

2

=6.16 units

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